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The effect of unstable correlations on portfolio diversification

11/09/2013

Chris Durack

Country Head of Hong Kong and Head of Institutional Asia Pacific

Purpose of this paper

The standard model used to determine a strategic asset allocation (SAA) relies on three main inputs for a set of asset classes: long run expected returns, expected annualised volatility and expected correlations.

In constructing portfolios, an optimisation problem is usually characterised by maximising long run expected returns subject to given levels of volatility in these returns. Or alternatively, minimising annualised volatility for a given expected long run return.

A principal argument of standard portfolio optimisation is that lower correlations provide scope for diversification within a portfolio. Particularly for those investors who prefer to meet a given expected return objective with minimum (acceptable) downside volatility, the level of diversification within a portfolio will matter a great deal.

In the context of long term modelling, there is an assumption of a long run correlation relationship between asset class returns. The purpose of this paper is to examine the data and call this assumption into question. If correlations prove to have unstable characteristics then what are the implications for portfolio construction and especially for expectations of diversification?

Overall, we find that by focussing on the behaviour of correlations in environments that may threaten the achievement of investment objectives, outcomes generated by a fixed SAA portfolio are inefficient. Instead there is scope for improved diversification outcomes to assist in achieving investment objectives from the perspective of recognizing what drives the conditional behaviour of asset classes.

A century of asset class performance

We examined one hundred years of monthly returns data to 31 December 2012 for the major asset classes. The return and standard deviation for each asset class for the full sample is reported in the following table.

Over the period, it can be readily seen that shares outperformed bonds and cash by a considerable margin, albeit with considerably higher volatility. In addition, the Australian asset classes outperformed their global counterparts. The data support the proposition of a positive long run risk-reward relationship. However, what is of interest in this paper is the pattern of how each asset class has generated its returns. The table below shows the correlation matrix for the asset classes over the full period.

Key observations

- Relative to Australian inflation, all asset classes with the exception of Australian bank bills display a very low average correlation.- The most strongly correlated asset classes on average are domestic and overseas shares. Overseas shares and overseas bonds also displayed on average a higher level of correlation.- While there was positive average correlation between the fixed income and cash asset classes, these were at levels indicating strong average diversification benefits.- Overall, when looking at the long term average correlations, it is readily apparent that overall mainly positive and low levels of correlation might be expected to assist in portfolio diversification.

The value of diversification

Perhaps a better question to ask is what value there might be in using long run average correlation data to help meet investor objectives. When do we want diversification benefits in the portfolio and for what purpose?

In line with previous papers dealing with asset allocation, it is helpful to start with a definition of an investment objective to determine what risks we might reasonably want to diversify away or at least reduce. In this regard, for investors seeking a meaningful money weighted real return over a realistic time frame, it seems reasonable to suggest that the following key risks might pose real threats to this objective:

- Different inflation regimes. Do asset classes behave differently (and relative to one another) in high, medium and low inflation environments?- Episodes of equity market volatility. In particular how effective can other asset classes guard against the downside volatility of equities?

To provide an initial overview of these issues, consider a portfolio that has a fixed strategic asset allocation. A feasible (and common) portfolio with 60% exposure to growth assets and 40% exposure to defensive assets was chosen for this purpose. Chart 1 shows the rolling three year performance of the SAA portfolio alongside rolling three year inflation outcomes. The dotted lines in the chart represent three (somewhat arbitrary) regimes of inflation. Namely, high inflation periods when rolling three year outcomes are above 4% p.a., moderate inflation periods where rolling three year outcomes are between 1% p.a. and 4% p.a. and low inflation periods when outcomes are below 1% p.a..p>

To generate a meaningful real rate of return, the first component of the return is to cover the rate of inflation. It can be readily observed that the spread of inflation outcomes over the last century is very wide with three year outcomes ranging between minus 8% p.a. and 16% p.a. Moreover, the rate of inflation experienced is persistent and occurs in “regimes” – the strong deflationary period shown in the chart occurred during the Great Depression and persistently high inflation outcomes occurred during and after periods of war as well as the oil driven shocks in the 1970s. Given the importance of delivering returns above inflation, it is natural to think about the behaviour of portfolios during different inflation regimes. Again the chart is helpful in illustrating the volatility in outcomes experienced over the century and shows a tendency for the fixed SAA portfolio to underperform the rate of inflation with a degree of regularity within different inflation regimes. While over the entire period, the portfolio on average performs above the rate of inflation, there are episodes of performance where investors suffered sustained negative real returns.

Chart 1

Source: GFD, Schroders

Equity market volatility is a disproportionate source of overall portfolio volatility in a fixed 60/40 SAA portfolio. As Chart 2 demonstrates, over the last 100 years, frequent episodes of negative equity market returns occur even when the time period is stretched over rolling three year periods. The average correlation benefits that are apparent in Table 2 above assist in dampening the overall volatility of the portfolio but it is less clear that these benefits are delivered at the right time. The Depression, the 1970s, the “tech wreck” and the GFC are clear examples of negative return periods for a fixed SAA portfolio, but these episodes do not comprehensively describe the periods of poor performance.

Chart 2

Source: GFD, Schroders

Conditional correlations

Given the shortcomings that the cursory inspection of a fixed SAA portfolio performance brings to light, a closer inspection of asset class correlations seems warranted. In order to do this, the data was partitioned to focus on the key sources for which diversification can assist in meeting portfolio objectives, i.e. delivering reliable real returns and protecting against equity drawdown events.

Correlations conditioned on inflation regime

Consistent with the data shown in Chart 1 above, correlation matrices were calculated for asset class performance in different rolling three year “regimes” of inflation:

- High inflation periods: when rolling three year outcomes are above 4% p.a.,- Moderate inflation periods: when rolling three year outcomes are between 1% p.a. and 4% p.a.; and- Low inflation periods: when rolling three year outcomes are below 1% p.a..

The correlations were then compared for differences relative to the average correlations experienced over the century. The results are summarised in Table 3 below.

Table 3

Sub Sample

Australian versus global shares

Australian versus global bonds

Australian shares versus bonds

Global shares versus bonds

Shares versus cash

Bonds versus cash

Notable changes versus inflation

Inflation greater than 4% p.a.

Higher(0.46 vs 0.40)

In line(0.18 vs 0.19)

Higher(0.25 vs 0.12)

Higher(0.36 vs 0.29)

In line

In line

Lower: cash(0.10 vs 0.19)

Inflation between 1% p.a. and 4% p.a.

Higher(0.51 vs 0.40)

In line(0.22 vs 0.19)

Lower(0.01 vs 0.12)

Lower(0.18 vs 0.29)

Slightly lower

In line

Significantly lower: cash(-0.03 vs 0.19)

Inflation less than 1% p.a.

Significantly lower(0.06 vs 0.40)

Slightly lower(0.14 vs 0.19)

Lower(0.03 vs0.12)

Higher(0.42 vs 0.29)

Lower

Lower

Significantly lower: cash(-0.39 vs 0.19)

Source: GFD, Schroders

Key:

“significantly higher (lower)” means a correlation coefficient greater (less) than 0.2 relative to the long run average.

“higher (lower)” means a correlation coefficient greater (less) than 0.05 relative to the long run average.

“in line” means a correlation coefficient within a range of 0.05 relative to the long run average.

Key observations

Overall when inflation is higher, there is a tendency for asset class correlations to increase with the exception of cash. It is notable that asset class volatility tends to be higher in outright terms for all asset classes with the exception of cash during these periods.

Conversely there is a tendency for asset class correlations to decrease in periods of low inflation. For periods of disinflation which dominate this sample, very large equity drawdowns contribute to lowering correlations while the performance of Australian shares was strong in relative terms versus global shares.

The implications for cash as a diversifying or hedging asset relative to inflation is particularly sensitive to the regime of inflation outcomes.

Correlations conditioned on Australian shares performance

Consistent with the data shown in Chart 2 above, correlation matrices were calculated for asset class performance in different rolling three year performance outcomes for Australian shares:

- High returns: when rolling three year outcomes are above one standard deviation,- Moderate periods: when rolling three year outcomes are within one standard deviation; and- Low return periods: when rolling three year outcomes are below one standard deviation.

The correlations were then compared for differences relative to the average correlations experienced over the century. The results are summarised in Table 4 below.

Table 4

Sub Sample

Australian versus global shares

Australian versus global bonds

Australian shares versus bonds

Global shares versus bonds

Shares versus cash

Bonds versus cash

Notable changes versus inflation

Below one standard deviation

Lower(0.25 vs 0.40)

In line(0.17 vs 0.19)

Significantly lower(-0.10 vs 0.12)

Higher(0.51 vs 0.29)

Significantly lower

Significantly lower

Higher for all shares and bondsSignificantly lower for cash(-0.70 vs 0.19)

Within one standard deviation

Higher(0.51 vs 0.40)

In line(0.19 vs 0.19)

In line(0.14 vs 0.12)

In line(0.28 vs 0.29)

In line

In line

In line

Above one standard deviation

Lower(0.32 vs 0.40)

Slightly higher(0.25 vs 0.19)

In line(0.13 vs 0.12)

In line(0.28 vs 0.29)

Higher

Higher for Aust bondsLower for global bonds

Higher for all shares and bondsSignificantly higher for cash(0.68 vs 0.19)

Source: GFD, Schroders

Key:

“significantly higher (lower)” means a correlation coefficient greater (less) than 0.2 relative to the long run average.

“higher (lower)” means a correlation coefficient greater (less) than 0.05 relative to the long run average.

“in line” means a correlation coefficient within a range of 0.05 relative to the long run average.

Key observations

When Australian shares are producing rolling three year returns within one standard deviation, correlation coefficients are quite consistent with the long term averages.

There is a propensity for correlations to be lower between asset classes when the Australian shares asset class is generating low returns below one standard deviation of its long term average. In particular in these environments, Australian bonds and cash have been particularly diversifying relative to cash and each other.

When Australian shares three year returns are particularly strong, there is an overall propensity for asset class correlations to rise. Of particular note is the very strong rise in the correlation of inflation and cash returns in strong equity markets and the converse of this phenomenon when equity markets are falling. When taken together with the inflation regime analysis above, the strategic role of cash in the portfolio seems to be highly sensitive to the environment in which a portfolio is being constructed.

What does the analysis lead to overall?

Conditional correlation matrices are different, and in some instances very importantly so, relative to the long run average correlation matrix.

The impact of equity volatility will continue to dominate a fixed SAA growth portfolio. This is evident in the conditional analysis of different inflation and equity market scenarios. Diversifying away from equities will not solve the problem relative to objectives as it will only trade average volatility for average lower returns without necessarily producing the same benefits in the way the pattern of returns is generated.

Historically, higher inflation periods have been associated with higher asset class volatility to the up and downside. Importantly, adding and subtracting cash from the portfolio is always sensitive to both equity and inflation environments.

Achieving real portfolio diversification

Is it possible to use information from conditional analysis of correlations to build portfolios? We see this issue as a corollary of our earlier paper in which we showed the behaviour of an asset class is (among other factors) a function of its valuation. In relation to equities we demonstrated that when the starting valuation is low, the probability of an above average subsequent three year return is higher and vice versa. The conditional distribution of returns for an asset class was therefore different to the unconditional distribution.

And so it is with correlations. If the behaviour of asset classes is conditional on their valuations then it follows that so will the conditionality of correlations. The important implication to be drawn here is that a long run SAA portfolio risks being under diversified relative to its objectives given that valuation information is not being discounted in the portfolio construction process.

We continue to argue that portfolio construction must use the current information available in the valuations of securities and asset classes to establish medium term (say three year) expectations. It is not appropriate to use long run averages as a proxy for this process. As we have shown for return distributions and now for correlations of these distributions, long run SAA portfolios are inefficient relative to their investors’ objectives due to their lack of incorporation of available valuation information to ensure their proper diversification.

Disclaimer

Opinions, estimates and projections in this article constitute the current judgement of the author as of the date of this article. They do not necessarily reflect the opinions of Schroder Investment Management Australia Limited, ABN 22 000 443 274, AFS Licence 226473 ("Schroders") or any member of the Schroders Group and are subject to change without notice. In preparing this document, we have relied upon and assumed, without independent verification, the accuracy and completeness of all information available from public sources or which was otherwise reviewed by us. Schroders does not give any warranty as to the accuracy, reliability or completeness of information which is contained in this article. Except insofar as liability under any statute cannot be excluded, Schroders and its directors, employees, consultants or any company in the Schroders Group do not accept any liability (whether arising in contract, in tort or negligence or otherwise) for any error or omission in this article or for any resulting loss or damage (whether direct, indirect, consequential or otherwise) suffered by the recipient of this article or any other person. This document does not contain, and should not be relied on as containing any investment, accounting, legal or tax advice.

Appendix:

Summary of Correlation Matrices: Conditional and Unconditional

The standard model used to determine a strategic asset allocation (SAA) relies on three main inputs for a set of asset classes: long run expected returns, expected annualised volatility and expected correlations.

In constructing portfolios, an optimisation problem is usually characterised by maximising long run expected returns subject to given levels of volatility in these returns. Or alternatively, minimising annualised volatility for a given expected long run return.

A principal argument of standard portfolio optimisation is that lower correlations provide scope for diversification within a portfolio. Particularly for those investors who prefer to meet a given expected return objective with minimum (acceptable) downside volatility, the level of diversification within a portfolio will matter a great deal.

In the context of long term modelling, there is an assumption of a long run correlation relationship between asset class returns. The purpose of this paper is to examine the data and call this assumption into question. If correlations prove to have unstable characteristics then what are the implications for portfolio construction and especially for expectations of diversification?

Overall, we find that by focussing on the behaviour of correlations in environments that may threaten the achievement of investment objectives, outcomes generated by a fixed SAA portfolio are inefficient. Instead there is scope for improved diversification outcomes to assist in achieving investment objectives from the perspective of recognizing what drives the conditional behaviour of asset classes.

Topics:

Important Information:
Opinions, estimates and projections in this article constitute the current judgement of the author as of the date of this article. They do not necessarily reflect the opinions of Schroder Investment Management Australia Limited, ABN 22 000 443 274, AFS Licence 226473 ("Schroders") or any member of the Schroders Group and are subject to change without notice. In preparing this document, we have relied upon and assumed, without independent verification, the accuracy and completeness of all information available from public sources or which was otherwise reviewed by us. Schroders does not give any warranty as to the accuracy, reliability or completeness of information which is contained in this article. Except insofar as liability under any statute cannot be excluded, Schroders and its directors, employees, consultants or any company in the Schroders Group do not accept any liability (whether arising in contract, in tort or negligence or otherwise) for any error or omission in this article or for any resulting loss or damage (whether direct, indirect, consequential or otherwise) suffered by the recipient of this article or any other person. This document does not contain, and should not be relied on as containing any investment, accounting, legal or tax advice. Schroders may record and monitor telephone calls for security, training and compliance purposes.

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